Seminars and Colloquia by Series

Riemann-Roch Theory for Directed Graphs

Series
SIAM Student Seminar
Time
Friday, November 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Spencer BackmanSchool of Mathematics, Georgia Tech
The talk will begin with an elementary geometric discussion of Riemann-Roch theory for sub-lattices of the integer lattice orthogonal to some positive vector. A pair of necessary and sufficient conditions for such a lattice to have the Riemann-Roch property will be presented. By studying a certain chip firing game on a directed graph related to the lattice spanned by the rows of its Laplacian I will describe a combinatorial method for checking whether a directed graph has the Riemann-Roch property. The talk will conclude with a presentation of arithmetical graphs, which after the application of a simple transformation, may be viewed as a special class of directed graphs. Examples from this class demonstrate that either, both or neither of the Riemann-Roch conditions may be satisfied for a directed graph. This is joint work with Arash Asadi.

A Minimax Problem in Almost Axisymmetric Flows

Series
SIAM Student Seminar
Time
Friday, November 12, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Mark SedjroSchool of Mathematics, Georgia Tech
Almost axisymmetric flows are derived from Boussinesq equations for incompressible fluids. They are supposed to capture special features in tropical cyclones. We establish an unusual minimax equality as the first step towards studying this challenging problem. I will review some basic techniques of the calculus of variations.

Global Stability of Dynamical Networks

Series
SIAM Student Seminar
Time
Friday, November 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ben WebbSchool of Mathematics, Georgia Tech
In this talk we consider the collective dynamics of a network of interacting dynamical systems and show that under certain conditions such dynamical networks have a unique global attractor. This involves a combination of techniques from dynamical systems theory as well as newly devised methods in graph theory. However, this talk is intended to be an introduction to both areas of mathematics with a focus on how the combination of the two is yielding new results in graph and dynamical systems theory.

When do random CSPs become hard?

Series
SIAM Student Seminar
Time
Friday, October 29, 2010 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ricardo RestrepoSchool of Mathematics, Georgia Tech
A constraint satisfaction problem (CSP) is an ensemble of boolean clauses, where satisfaction is obtained by an assignment of the variables if every clause is satisfied by such assignment. We will see that when such CSP is arranged following certain random structure, the Fourier expansion of the corresponding clauses allows us to understand certain properties of the solution space, in particular getting a partial understanding of when the 'usual suspects' of the drastical failure of all known satisfiability algorithms, namely long range correlations and clustering, appear. Based in joint work with Prasad Tetali and Andrea Montanari.

On nonparametric multivariate statistical process control charts

Series
SIAM Student Seminar
Time
Friday, October 22, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Giang DoSchool of Mathematics, Georgia Tech
Statistical Process Control Charts are key tools in monitoring and controlling production processes to achieve conforming, high quality products. We will conduct a literature review on the Nonparametric Multivariate Statistical Process Control Charts to see what has been done in the area and how the methods have been applied.

The entropy production problem and Villani's conjecture

Series
SIAM Student Seminar
Time
Friday, October 8, 2010 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Amit EinavSchool of Mathematics, Georgia Tech
In 1956 Mark Kac published his paper about the Foundation of Kinetic Theory in which he gave a mathematical, probabilistic description of a system of N particles colliding randomly. An interesting result that was found, though not causing any surprise, was the convergence to the stable equilibrium state. The question of the rate of the L2 convergence interested Kac and he conjectured that the spectral gap governing the convergence is uniformly bounded form below as N goes to infinity. While this was proved to be true, and even computed exactly, many situations show that the time scale of the convergence for very natural cases is proportional to N, while we would hope for an exponential decay. A different approach was considered, dealing with a more natural quantity, the entropy. In recent paper some advancement were made about evaluating the rate of change, and in 2003 Villani conjectured that the corresponding 'spectral gap', called the entropy production, is of order of 1/N. In our lecture we'll review the above topics and briefly discuss recently found results showing that the conjecture is essentially true.

Small Noise: Dynamical Systems and Probability put together

Series
SIAM Student Seminar
Time
Friday, September 24, 2010 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Serjio AlmandaSchool of Mathematics, Georgia Tech
In this talk I will outline a topic that has been of interest due to its applicability in physics and engineering. The so called small noise model is a very technical subject that lies in the center of probability theory and usually study thorough a large deviations approach. I will explain this terminology and why is the correlation with dynamical systems so strong. Recent developments will be given at the end if time allows.

A brief introduction to copulas and related problems

Series
SIAM Student Seminar
Time
Friday, April 2, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ruodu WangSchool of Mathematics, Georgia Tech
A copula C of n arbitrary random variables X_1, ..., X_n contains all the information about their dependence. First I will briefly introduce the definition, basic properties and elementary examples of copulas, as well as Sklar's Theorem (1959). Then I will present a family of multivariate copulas whose marginal copula belongs to a family of extreme copulas. Finally I will discuss a minimization problem related to copula, which is still open. The talk should be easy to understand for all level audience who have knowledge of basic probability theory

Pages